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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 2: Q.2.132 (page 193)

Solve the compound inequality. Graph the solution and write the solution in interval notation. $\frac{3}{4} x - 3 鈮� 3 o r \frac{2}{5} (x + 10) 鈮� 0$

Short Answer

Expert verified

$S o l u t i o n : T r u e f o r a l l x I n t e r v a l N o t a t i o n : (- 鈭�, 鈭�)$

Step by step solution

01

Step 1. Given information

$\frac{3}{4} x - 3 鈮� 3 o r \frac{2}{5} (x + 10) 鈮� 0$

02

Step 2.Solve each Inequalities

$\frac{3}{4} x - 3 鈮� 3 o r \frac{2}{5} (x + 10) 鈮� 0 \frac{3}{4} x - 3 + 3 鈮� 3 + 3 \frac{5}{2} 脳 \frac{2}{5} (x + 10) 鈮� 0 脳 \frac{5}{2} \frac{3}{4} x 鈮� 6 x + 10 鈮� 0 \frac{3}{4} x 脳 \frac{4}{3} 鈮� 6 脳 \frac{4}{3} x + 10 - 10 鈮� 0 - 10 x 鈮� 8 x 鈮� - 10$

03

Step 3. Graph the Solution

Graph of $\frac{3}{4} x - 3 鈮� 3$

Graph of $\frac{2}{5} (x + 10) 鈮� 0$

By merging the above graphs we get it is true for all x

04

Step 4. Solution and Interval Notation

$S o l u t i o n : T r u e f o r a l l x I n t e r v a l N o t a t i o n : (- 鈭�, 鈭�)$

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